Pages

Thursday, February 5, 2015

I took this photo of a worker honeybee gathering nectar and pollen about a week ago. I usually get interested in various subjects for a brief amount of time, before moving on to the next unexpected topic, and the subject of bees is no different. In any case, I read up on a handful of Wikipedia articles, and I called it a day, as far as researching bees.

I might drone on about the recent decline of honeybees, their relationship to virtually all human agriculture, and perhaps how this can be a dark horse factor in the unsustainable nature of human civilization -- but I won't go past that run-on sentence.

I want to write about numbers. In my "extensive research" -- the skimming of Wikipedia mentioned earlier -- I learned that there are two kinds of worker bees. There are the ones that don't lay eggs, and there are the few worker bees who lay unfertilized eggs, which hatch into drones. Worker bees are genetically female, if you hadn't known that already. Drones are male bees.

Of course, there's the queen bee, whose eggs are fertilized by drones from other hives. The queen's offspring hatch into worker bees and future queen(s).

Let's get to numbers, starting with the Drone, a male, to whom we'll refer with a capital D -- 1.

The Drone bee has one parent: A laying worker bee, a female -- also 1.

The Drone has two grandparents: The hive queen (female) and an outsider drone (male) -- 2.

The Drone has three great-grandparents: the previous hive queen and an outsider drone, as well as an outsider laying worker bee -- 3.

The Drone has five great-great-grandparents: The previous-previous hive queen and an outsider drone, an outsider laying worker, and an outsider queen with a drone from another hive (perhaps the Drone's hive) -- 5. The great-great-grand-drones are different bees because a drone can only mate with one queen; he dies soon after.

The Drone has eight great-great-grandparents: The previous-previous-previous hive queen and an outsider drone, an outsider laying worker, an outsider queen and an unrelated drone, an outsider queen with an unrelated drone, and an outsider laying worker -- 8. At this point, the outsider laying workers might have come from the same outsider hive, or there is a small chance that a single outsider worker might have laid multiple drone eggs for the next generation(s). The chance for redundant ancestors for the Drone becomes greater at this point on.

In any case, the Drone's family tree is basically the Fibonacci sequence: 1 1 2 3 5 8 13 21 etc. Any given worker or queen has a family tree that includes one self, two parents, three grandparents, five great-great grandparents, etc., or 1 2 3 5 8 13 21 34, etc.

For those uninitiated concerning the Fibonacci sequence, I can't provide any useful information. It's a sequence that occurs in nature, and humans caught on only fairly recently, a thousand years ago or so -- because it was a cool pattern, I suppose. You take 1, which equals 1. You add those previous numbers, and you get 2. You add the most recent two numbers, and you get 3. Then you get 5. Then you get 8. And so on, and so forth.

Humans and animals who come from fertilized eggs just have an exponential amount of ancestors: 1 self, 2 parents, 4 grands, 8 greats, 16, 32, 64, 128, etc. The fun part, putting polygamy/incestual humor aside, is to identify the first possible redundancy in a fertilized egg family tree. Like the Drone, we'll call this subject "the Human."

The Human has one self.

The Human has two parents.

The Human has four grandparents, but there is a chance that the grandfathers and/or the grandmothers might be the same person. That took three generations for a small chance at polygamy/serial monogamy, with incest a generation after. It took male bees six generations, and female bees five, from self to a small chance at having redundant ancestors.

In all likelihood, actual ancestor redundancies occur as the great- prefixes accumulate. The Human's maternal great-great-great grandparents might also be the Human's paternal great-great-great-great grandparents. It is very likely that each person has multiple redundant ancestors.

Since our ancestors are more-or-less exponential, it is possible, if not probable, that every civilized person's family tree overlaps with other civilized person's family tree, no matter their current nationality or ethnicity, within a few centuries to a thousand years or so, tops. Isolated populations are another story, and civilization's collective family tree overlaps with their ancestors probably thousands of years earlier.

It's the same with bees, of course. With other bees, to be clear.

In any case, I had nothing substantial to write today, the 5th, so I wrote about numbers. And bees. I don't even find numbers that interesting, that often. I still find bees fairly interesting, especially their honey. I should have written about good, local bee honey, the kind you'd find at a farmer's market.